Optimized auxiliary oscillators for the simulation of general open quantum systems

Mascherpa, F.; Smirne, Andrea; Somoza, Alejandro D.; Fernández-Acebal, P.; Donadi, Sandro; Tamascelli, Dario; Huelga, Susana F.; Plenio, Martin B.

doi:10.1103/physreva.101.052108

Cited by 80 publications

(53 citation statements)

References 111 publications

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“…Finally, an open problem relating to construction of the master equation is how to convert between the pathological and Lindblad form for when the OQS couples to more than two discrete modes with complex coefficients; as far as we are aware, no generalized form of transformation matrix allowing for the conversion has been determined beyond this case (although see, perhaps, the related inversion problem explored in Appendix B of Ref. [49]). Therefore future work in this area could focus on developing a systematic approach to regularizing the master equation for arbitrarily complicated environmental structures, which in itself would likely rely on a numerical implementation.…”

Section: Discussionmentioning

confidence: 99%

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Pleasance

Garraway

Petruccione

2020

Phys. Rev. Research

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We develop an exact framework for describing the non-Markovian dynamics of an open quantum system interacting with an environment modeled by a generalized spectral density function. The approach relies on mapping the initial system onto an auxiliary configuration, comprising the original open system coupled to a small number of discrete modes, which in turn are each coupled to an independent Markovian reservoir. Based on the connection between the discrete modes and the poles of the spectral density function, we show how expanding the system using the discrete modes allows for the full inclusion non-Markovian effects within an enlarged open system whose dynamics is governed by an exact Lindblad master equation. Initially we apply this result to obtain a generalization of the pseudomode method [B. M. Garraway, Phys. Rev. A. 55, 2290 (1997)] in cases where the spectral density function has a Lorentzian structure. For many other types of spectral density function, we extend our proof to show that an open system dynamics may be modeled physically using discrete modes which admit a non-Hermitian coupling to the system and for such cases determine the equivalent master equation to no longer be of Lindblad form. For applications involving two discrete modes, we demonstrate how to convert between pathological and Lindblad forms of the master equation using the techniques of the pseudomode method.

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Section: Discussionmentioning

confidence: 99%

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Pleasance

Garraway

Petruccione

2020

Phys. Rev. Research

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“…These methods allow for the description of features that were not accurately described by approximate methods, such as the Markov, Bloch-Redfield or perturbative expansion techniques [ 18 ]. Among them we mention the hierarchical equations of motion (HEOM) [ 32 , 33 , 34 ], path integral methods [ 35 , 36 , 37 ], Dissipation-Assisted Matrix Product Factorization [ 38 ], and pseudo-modes related transformations [ 23 , 39 , 40 ].…”

Section: Introductionmentioning

confidence: 99%

Excitation Dynamics in Chain-Mapped Environments

Tamascelli

2020

Entropy

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The chain mapping of structured environments is a most powerful tool for the simulation of open quantum system dynamics. Once the environmental bosonic or fermionic degrees of freedom are unitarily rearranged into a one dimensional structure, the full power of Density Matrix Renormalization Group (DMRG) can be exploited. Beside resulting in efficient and numerically exact simulations of open quantum systems dynamics, chain mapping provides an unique perspective on the environment: the interaction between the system and the environment creates perturbations that travel along the one dimensional environment at a finite speed, thus providing a natural notion of light-, or causal-, cone. In this work we investigate the transport of excitations in a chain-mapped bosonic environment. In particular, we explore the relation between the environmental spectral density shape, parameters and temperature, and the dynamics of excitations along the corresponding linear chains of quantum harmonic oscillators. Our analysis unveils fundamental features of the environment evolution, such as localization, percolation and the onset of stationary currents.

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“…The contribution of the first logarithmic term cancels the first term in Eq. (33). Moreover, the contribution of the second term cancels the classical part of the heat current, while those coming from the third term vanish.…”

Section: Evaluation Of the Heat Current In The Overdamped Limitmentioning

confidence: 94%

“…The Markovian limit (ω c → ∞) can be easily obtained by replacing the factors ω c /(ω c + ω d ) by 1 in Eqs. (31) and (33) and noting that the roots λ ± satisfy lim…”

Section: Evaluation Of the Heat Current In The Overdamped Limitmentioning

confidence: 99%

Heat transport in overdamped quantum systems

et al. 2020

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We obtain an analytical expression for the heat current between two overdamped quantum oscillators interacting with local thermal baths at different temperatures. The total heat current is split into classical and quantum contributions. We show how to evaluate both contributions by taking advantage of the timescale separation associated with the overdamped regime and without assuming the usual weak-coupling and Markovian approximations. We find that nontrivial quantum corrections survive even when the temperatures are high compared to the frequency scale relevant for the overdamped dynamics of the system.

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Optimized auxiliary oscillators for the simulation of general open quantum systems

Cited by 80 publications

References 111 publications

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes

Excitation Dynamics in Chain-Mapped Environments

Heat transport in overdamped quantum systems

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